Hip/Valley Roof Joinery
3D Models of Joints

 Close-up images of joinery details related to the models to be posted in the near future.

Theoretical Angles ... 3D Models of Interlocking Tetrahedra
Interlocking Tetrahedra modeling the Backing Angle
Interlocking Tetrahedra modeling Prow Roof Stud Compound Angle
Interlocking Tetrahedra modeling Housing and Tenon Chamfer Cut Angles

Since the lines of intercept and angles between the planes of the proposed joints are known, the joint faces can be developed and 3D models created.

Angle values may be solved using Lag or an equivalent calculator, or by employing the methods outlined in DEVELOPMENTS

Models vary in scope, from simple developments illustrating the fundamental geometry of the roof to the detailed examples below.

Valley Foot meets Common Rafter
Preliminary compound angle cuts and layout

Bottom shoulder: Miter = R4P , Blade Angle = A5P
Plumb Face: Miter = 90 - R1 , Blade Angle = DD

Valley Foot meets Common Rafter
Compound angle and housing chamfers

Chamfers are perpendicular to the compound face

Tenon: Valley Foot meets Common Rafter

Tenon is perpendicular to the compound face

Common Rafter section showing
mortise to receive tenon at Valley Foot

Main Pitch angle SS at rafter foot is to the right
Housing angle to bottom edge of rafter = P6
 The housing angle for the related joint Valley Foot meets Wall slopes at R5P with respect to level.

Valley Peak meets Main Purlin
Preliminary compound angle cuts and layout

 The tenon in the following two views is cut square with respect to the compound face to the left in the image above.

Valley Peak meets Main Purlin
View of Tenon from bottom shoulder

Valley Peak meets Main Purlin
View of tenon on Valley meets Valley side

Side Views of Valley Tenons
Left: Foot meets Common Rafter
Right: Peak meets Main Purlin

End Views of Valley Tenons
Left: Peak meets Main Purlin
Right: Foot meets Common Rafter

Mortise: Valley Peak meets Main Purlin

 A jig similar in shape to the housing illustrated above was used to project the layout for the mortise "on the round" to achieve the joint in the image below.

Mortise: Valley Peaks meet at Main Purlin

 The following sets of images depict models of the joinery required for Valleys meet at Center Post Ridge Beams meet Valley Purlins meet Valley

Models of Valley Roof Sections

Valley Peaks meet at Center Post
Left: Preliminary compound angle cuts
Right: Bird's-Mouth cut for Center Post

Valley Section: the peak is to the left
Backing angle and Mortise layouts
Left: Jack Purlin   Right: Jack Rafter

 Left: Jack rafter compound angle Center: Jack purlin compound angle Right: Jack Purlin tenon layout. The shaded areas shown on the model to the right will be removed, square cutting the bottom face of the tenon.

Valley Peak meets Ridge Beam
Sketch of Intersection

Main Pitch: 10/12         Adjacent Pitch: 13/12
Angle viewded in plan between ridge lines: 90°

Plan View of Intersection

Preliminary compound angles and layout

Valley with Backing Angles
and finished faces at peak

Valley with Backing Angles
and finished faces at peak

Irregular Hips meet at Center Post

Plan: Irregular Octagon
Common Pitches
Left Hip rafter, Left Side: 8 9/16 ÷ 12
between Hip rafters Center: 7 17/32 ÷ 12
Right Hip rafter, Right Side: 7 1/2 ÷ 12

 The Hip rafters are offset to make the post intercept the long axes of the Hip rafters at right angles.